Hafnium (Hf) has six naturally occurring isotopes: 0.16% of 174Hf, with an atomic weight of 173.940 amu; 5.26% of 176Hf, with an atomic weight of 175.941 amu; 18.60% of 177Hf, with an atomic weight of 176.943 amu; 27.28% of 178Hf, with an atomic weight of 177.944 amu; 13.62% of 179Hf, with an atomic weight of 178.946 amu; and 35.08% of 180Hf, with an atomic weight of 179.947 amu. Calculate the average atomic weight of Hf.

178.463 amu

Explanation:

Average atomic weight of Hafnium is calculated as follows;

[(0.0016 × 173.940) + (0.0526 × 175.941) + (0.186 × 176.943) + (0.2728 × 177.944) + (0.1362 × 178.946) + (0.3508 × 179.947)] =0.278 + 9.234 + 32.911 + 48.543 + 24.372 + 63.125 = 178.463 amu

Therefore, average atomic weight of Hafnium is 178.463 amu

a: 45.9 meters

b: 4.29 seconds

step-by-step explanation:

a: h(t)=1/2(-9.8)(3)^2+0(3)+90

h(t)=-4.9(3)^2+90

h(t)=-44.1+90

h(t)=45.9 meters

b: 0=1/2(-9.8)(t^2)+0t+90

0=-4.9t^2+90

-90=-4.9t^2

18.37=t^2

t=4.29 seconds

in the second question, the numbers aren't exact, but they're a close approximation.